Explanation:
we need Pythagoras for right-angled triangles
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
we also need to remember that the sum of all angles in a quadrilateral (4-sided shape) is 360°.
so, as 3 angles in the main quadrilateral are 90°, so is also the 4th angle. and that makes the quadrilateral a regular rectangle.
we know the length of the rectangle (15 ft).
the width is also the second leg of the attached right-angled triangle.
so, we know
13² = 5² + (leg2)²
169 = 25 + (leg2)²
144 = (leg2)²
leg2 = sqrt(144) = 12 ft
the total area is
the area of the rectangle
+
the area of the triangle
the area of the rectangle is
length × width = 15 × 12 = 180 ft²
the area of the right-angled triangle is
leg1 × leg2 / 2 = 5 × 12 / 2 = 5×6 = 30 ft²
the total area is
180 + 30 = 210 ft²
FYI - a different way is to directly calculate the area of the trapezoid :
(base1 + base2)×height/2
height = the width of the rectangle or leg2 of the right-angled triangle.
so, we have
(15 + (15 + 5))×12/2 = (15 + 20)×6 = 35×6 = 210 ft²